Hyperspace travel is a norm in Star Wars universe. Even small ships have that capability and without this capability galactic-scale economy isn't possible.

My educated estimates say that at any point of time at least billions of ships are in hyperspace across the galaxy. Now, talk about economic hubs like Coruscant during Clone Wars Era. The number of ships arriving here should be enormous. Millions in an hour? If one person small ship can have warping capability, then the number can exceed even billions in a peak hour. You can go shopping on a neighbor planet five times a day or you can live on a cheap planet even if you have a job on Coruscant (there are public transport cabs featured in Rebels TV show in case you aren't rich enough to have own ship).

Now, the famous quote:

"Traveling through hyperspace ain't like dusting crops, boy! Without precise calculations we could fly right through a star or bounce too close to a supernova, and that'd end your trip real quick, wouldn't it?"

That's fine. Calculations prevent you from hitting a star, supernova or planet which are already on map, but how does a ship avoid hitting another ship? Provided that number of ships arriving near a planet is that much high, the probability of two ships jumping to the same co-ordinate can't be zero. In fact, the probability should be very very high.

Is there a central body which controls the traffic by coordinating the hyperspace calculations of different ships? This seems unlikely because everyone seems to go anywhere they want while maintaining the destination privacy (there are countless examples). Or, is there really a traffic control body and those who travel privately actually gamble? Is there any other protocol if not traffic control body?

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This is one time where I'll assert that out of universe, non-canon citing answer is superior to anything written in canon.

Provided that number of ships arriving near a planet is that much high, the probability of two ships jumping to the same co-ordinate can't be zero. In fact, the probability should be very very high

Actually, the odds of hitting another ship coming out of hyperspace, even around Coruscant, are approximately three thousand seven hundred and twenty to one. Wait, no, that's chances in an asteroid field.

Let's put a upper bound on your odds, following in the illustrious footsteps of that greatest of actuarial geniouses, C-3PO.

Radius of Coruscant: ~6,000km (EU src: Coruscant and the Core Worlds)

We don't know the distance between planets in that system from canon, but just for realism let's pretend the next planet is no further than Mars is from Earth - that being ~0.5AU, or approximately 75 million km

Let's charitably pretend that no ships can hyperspace closer to Coruscant than 1 million km, an no further than 74 million km, so that they don't have a chance to accidentally miss and hit either Coruscant or its nearest planet, if any.

Let's assume that the area that the ships are allowed to hyperspace out is approximately a hemisphere (with 1 Mil km heart cut out) 74 Mil km in radius, extending towards outside of their system.

The volume of a full sphere would be ~1.7 × 1024 km3. We can subtract the fully-insignificant 4.19 × 1018 core sphere of 1M km around Coruscant, resulting in ~1.6999958 × 1024. OK, seriously, let's round up back to 1.7, and divided in 2 to get the hemisphere, we get 0.85 × 1024 km3 to make a hyperspace jump to.

The largest dimension (length) of one of the largest capital ships (Executor class Drednaught, aka Super Star Destroyer) is 19km.

Since we're working on lower bound of odds, let's assume the WORST case scenario to increases the chances of collision, and pretend that SSD is a perfect sphere the size of 20km (as we saw in Empire Strikes Back, the fact that they are not perfect spheres, means SDs can actually avoid collision at distances far less than their lengths).

This exaggregated estimate gives us a volume of a spherical SSD as 4189 km3. Let's make that 10,000 km3 for further simplicity.

Now, let's pretend that (again, to exaggregate the danger, and thus obtain the lower bounds) that 10,000 ships - EACH of which is at least as large as our spherical SSD - hyperspace jump into our permitted hemispherical area, haphasardly, at random. AT THE SAME TIME. AND don't land.

Unless I completely misremember my stats class (very likely, and please correct me in the comments), the odds of two ships colliding, in that volume of space, are far lower than 1 in 1010

In reality, you can of course hypserpace out far more out - a typical solar system (using Sol as example) has FAR more space (Pluto is 30-40AU from the Sun, but that'd result in Stack Overflow should I compute the odds). Unless I miss something in my calculations, this would decrease the odds of collision to an upper bound of ~ 1 in 1015

Awesome effort, but you ignored a big thing: People's choice. Why would someone jump 70 million Km away if they can jump to 1 million Km away from the planet. If you consider people's choices, the available volume of space won't be high.
– I Love You 3000Jan 6 '16 at 5:01

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@SS-3 - actually, the reverse. "I'm coming up on Coruscant. I know every lazy idiot will jump out 1Mil km away. Instead of getting stuck in traffic, let me jump 5Mil away, and cruise in in comfort, at the cost of 1 extra minute of lightspeed travel. How do I know that? Because that's exactly what I - and many people I know - think and do when parking my car in a shopping mall parking lot
– DVK-on-Ahch-ToJan 6 '16 at 5:15

@SS-3 - and that's even assuming people are able to jump out THAT precisely, and not simply be strewn around 1Mil km pattern around where they wanted to jump out. Remember Captain Needa?
– DVK-on-Ahch-ToJan 6 '16 at 5:17

Parking analogy is great except people need to think about avoiding crash, not traffic congestion. You still didn't answer the question.
– I Love You 3000Jan 6 '16 at 8:06